Source labels openChecked July 26, 2026

Erdős Problem 319

What is the size of the largest $A\subseteq\{1, \dots, N\}$ such that there is a function $\delta : A \to \{-1, 1\}$ such that $\sum_{n\in A} \frac{\delta n}{n} = 0$ and $\sum_{n\in A'}\frac{\delta n}{n} \neq 0$ for all non-empty $A'\subsetneq A$ .

Combinatorics AMS 5

Mathematical statement

What is the size of the largest $A\subseteq\{1, \dots, N\}$ such that there is a function $\delta : A \to \{-1, 1\}$ such that

\sum_{n\in A} \frac{\delta n}{n} = 0

and

\sum_{n\in A'}\frac{\delta n}{n} \neq 0

for all non-empty $A'\subsetneq A$ .

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_319

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_319 (N : ℕ) : IsGreatest    { #A | (A) (_ : A ⊆ Finset.Icc 1 N)      (_ : ∃ δ : ℕ → ℤˣ, ∑ n ∈ A, (δ n : ℚ) / n = 0 ∧        ∀ A' ⊂ A, A'.Nonempty → ∑ n ∈ A', (δ n : ℚ) / n ≠ 0) }    answer(sorry) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/319background